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Ground state octupole correlation energies with effective forces

The ground state octupole correlation energy is computed with the D1M variant of the Gogny force in different theoretical frameworks and analyzed in detail. First I consider the correlation energy gained at the mean field level by breaking reflection symmetry. Next I consider the energy gain coming from symmetry (parity) restoration and finally I analyze the ground state correlation energy after configuration mixing with axially symmetric octupole states. The impact of the latter on theoretical binding energies indicates that octupole correlations do not affect in a significant way the trend and systematic of binding energies and therefore can not improve the performance of theoretical models in this respect. In particular, the too-large "shell gaps" predicted by self-consistent mean field models and relevant in astrophysics scenarios are not altered by the octupole correlations.